A graph \(G\)  is perfect if for every induced subgraph \(H\)  of \(G\) , \(\chi (H)=\omega (H)\) . The Weak Perfect Graph Theorem [1]}
asserts that \(G\)  is perfect iff its complement \(G^c\)  is perfect. The Strong Perfect Graph Theorem [2]} asserts
that \(G\)  is perfect iff \(G\)  is
a Berge graph, namely neither \(G\)  nor \(G^c\)  contains an induced cycle of odd length greater than 3. The class of perfect graphs
is a remarkable class of graphs with profound connections in mathematics, theoretical computer science and optimization.
There is also a rich area of graph theory devoted to the study of graphs with forbidden induced subgraphs, and perfect graphs
play a central role in this study.
